The bilinear derivative method developed by Hirota is a powerful and
direct approach to construct exact solution of nonlinear equations.
Once a nonlinear equation is written in bilinear forms by a
dependent variable transformation, then multi-soliton solutions are
usually obtained [1]}-[2]}. It was based on Hirota
forms that Nakamura proposed a convenient way to construct a kind of
quasi-periodic solutions of nonlinear equations [3]}, [4]},
where the periodic wave solutions of the KdV equation and the
Boussinesq equation were obtained. Such a method indeed exhibits
some advantages. For example, it does not need any Lax pairs and
Riemann surface for the considered equation, allows the explicit
construction of multi-periodic wave solutions, only relies on the
existence of the Hirota's bilinear form, as well as all parameters
appearing in Riemann matrix are arbitrary. Recently, further
development was made to investigate the discrete Toda lattice,
(2+1)-dimensional Kadomtsev-Petviashvili equation and
Bogoyavlenskii's breaking soliton equation [5]}-[6]}.
However, where repetitive recursion and computation must be
preformed for each equation [3]}-[6]}.
